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Forecasting seeing and parameters of long-exposure images by means of ARIMA

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Abstract

Atmospheric turbulence is the one of the major limiting factors for ground-based astronomical observations. In this paper, the problem of short-term forecasting seeing is discussed. The real data that were obtained by atmospheric optical turbulence (OT) measurements above Mount Shatdzhatmaz in 2007–2013 have been analysed. Linear auto-regressive integrated moving average (ARIMA) models are used for the forecasting. A new procedure for forecasting the image characteristics of direct astronomical observations (central image intensity, full width at half maximum, radius encircling 80 % of the energy) has been proposed. Probability density functions of the forecast of these quantities are 1.5–2 times thinner than the respective unconditional probability density functions. Overall, this study found that the described technique could adequately describe temporal stochastic variations of the OT power.

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Notes

  1. As a result of the linearity, E[x i ]=0 in this section without loss of generality.

  2. Inherently, the likelihood value corrected by the number of parameters.

  3. That is one of the criteria for model identification adequateness.

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Acknowledgements

The author is grateful to all the people of the MASS group at Sternberg Astronomical Institute. Moreover, the author would like to give special thanks to B. Safonov and V. Kornilov for the valuable discussions on early drafts of this paper. Lastly, the author highly appreciates the efforts of the anonymous reviewer to make the present paper more understandable to readers.

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  1. Sternberg Astronomical Institute, Lomonosov Moscow State University, Universitetsky pr., 13, Moscow, 119991, Russia

    Matwey V. Kornilov

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Kornilov, M.V. Forecasting seeing and parameters of long-exposure images by means of ARIMA. Exp Astron 41, 223–242 (2016). https://doi.org/10.1007/s10686-015-9485-7

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